cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A120165 a(n) = 7 + floor((1 + Sum_{j=1..n-1} a(j))/4).

Original entry on oeis.org

7, 9, 11, 14, 17, 21, 27, 33, 42, 52, 65, 81, 102, 127, 159, 199, 248, 310, 388, 485, 606, 758, 947, 1184, 1480, 1850, 2312, 2890, 3613, 4516, 5645, 7056, 8820, 11025, 13782, 17227, 21534, 26917, 33647, 42058
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.
Cf. A120160 - A120164, A120166 - A120169.

Programs

  • Magma
    function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/4);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
A120165:= func< n | g(n, 7, 1) >;
[A120165(n): n in [1..60]]; // G. C. Greubel, Sep 09 2023
  • Maple
    A[1]:= 7: S:= 7:
for n from 2 to 100 do A[n]:= floor((29 + S)/4); S:= S + A[n] od:
seq(A[i],i=1..100); # Robert Israel, Mar 20 2017
  • Mathematica
    a = {7}; Do[AppendTo[a, Floor[(29 + Total@ a)/4]], {i, 2, 40}]; a (* Michael De Vlieger, Mar 20 2017 *)
  • SageMath
    @CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
def A120165(n): return f(n, 7, 1)
[A120165(n) for n in range(1, 61)] # G. C. Greubel, Sep 09 2023

Formula

a(n) ~ c (5/4)^n with c approximately 5.5905081519. - Robert Israel, Mar 20 2017

A120171 a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/5).

Original entry on oeis.org

2, 2, 3, 3, 4, 5, 6, 7, 8, 10, 12, 14, 17, 20, 24, 29, 35, 42, 50, 60, 72, 87, 104, 125, 150, 180, 216, 259, 311, 373, 448, 537, 645, 774, 929, 1114, 1337, 1605, 1926, 2311, 2773, 3328, 3993, 4792, 5750, 6900, 8280, 9936, 11923, 14308, 17170, 20604, 24724, 29669
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088.

Programs

  • Magma
    function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/5);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
A120171:= func< n | g(n, 2, 1) >;
[A120171(n): n in [1..60]]; // G. C. Greubel, Dec 25 2023
  • Mathematica
    f[s_] := Append[s, Floor[(11 + Plus @@ s)/5]]; Nest[f, {2}, 53] (* Robert G. Wilson v, Jul 08 2006 *)
  • SageMath
    @CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//5
def A120171(n): return f(n, 2, 1)
[A120171(n) for n in range(1, 61)] # G. C. Greubel, Dec 25 2023

Extensions

More terms from Robert G. Wilson v, Jul 08 2006

A120184 a(1)=8; a(n)=floor((48+sum(a(1) to a(n-1)))/6).

Original entry on oeis.org

8, 9, 10, 12, 14, 16, 19, 22, 26, 30, 35, 41, 48, 56, 65, 76, 89, 104, 121, 141, 165, 192, 224, 261, 305, 356, 415, 484, 565, 659, 769, 897, 1047, 1221, 1425, 1662, 1939, 2262, 2639, 3079
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A112088, A072493.

Programs

  • Mathematica
    nxt[{t_,a_}]:=With[{c=Floor[(48+t)/6]},{t+c,c}]; NestList[nxt,{8,8},40][[All,2]] (* Harvey P. Dale, Apr 07 2019 *)

A120147 a(n) = 23 + floor( 1 + Sum_{j=1..n-1} a(j)/2 ).

Original entry on oeis.org

23, 35, 52, 78, 117, 176, 264, 396, 594, 891, 1336, 2004, 3006, 4509, 6764, 10146, 15219, 22828, 34242, 51363, 77045, 115567, 173351, 260026, 390039, 585059, 877588, 1316382, 1974573, 2961860, 4442790, 6664185, 9996277, 14994416
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Mathematica
    nxt[{t_,a_}]:=Module[{k=Floor[(47+t)/2]},{t+k,k}]; NestList[nxt,{23,23},40][[All,2]] (* Harvey P. Dale, Oct 29 2020 *)
  • SageMath
    @CachedFunction
def A120147(n): return 23 + (1 + sum(A120147(k) for k in range(1,n)))//2
[A120147(n) for n in range(1, 61)] # G. C. Greubel, May 30 2023

A120148 a(n) = 25 + floor( Sum_{j=1..n-1} a(j)/2 ).

Original entry on oeis.org

25, 37, 56, 84, 126, 189, 283, 425, 637, 956, 1434, 2151, 3226, 4839, 7259, 10888, 16332, 24498, 36747, 55121, 82681, 124022, 186033, 279049, 418574, 627861, 941791, 1412687, 2119030, 3178545, 4767818, 7151727, 10727590, 16091385
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Mathematica
    nxt[{t_,a_}]:=Module[{c=25+Floor[t/2]},{t+c,c}]; NestList[nxt,{25,25},40][[;;,2]] (* Harvey P. Dale, May 17 2023 *)
  • SageMath
    @CachedFunction
def A120148(n): return 25 + sum(A120148(k) for k in range(1, n))//2
[A120148(n) for n in range(1, 61)] # G. C. Greubel, May 31 2023

A120150 a(n) = 3 + floor((2 + Sum_{j=1..n-1} a(j))/3).

Original entry on oeis.org

3, 4, 6, 8, 10, 14, 18, 24, 32, 43, 57, 76, 102, 136, 181, 241, 322, 429, 572, 763, 1017, 1356, 1808, 2411, 3214, 4286, 5714, 7619, 10159, 13545, 18060, 24080, 32107, 42809, 57079, 76105, 101473, 135298, 180397, 240529
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

A120151 a(n) = 5 + floor( Sum_{j=1..n-1} a(j)/3 ).

Original entry on oeis.org

5, 6, 8, 11, 15, 20, 26, 35, 47, 62, 83, 111, 148, 197, 263, 350, 467, 623, 830, 1107, 1476, 1968, 2624, 3499, 4665, 6220, 8293, 11058, 14744, 19658, 26211, 34948, 46597, 62130, 82840, 110453, 147271, 196361, 261815, 349086, 465448, 620598, 827464, 1103285
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Magma
    function f(n,a,b)
  t:=0;
    for k in [1..n-1] do
       t+:= a+Floor((b+t)/3);
     end for;
  return t;
end function;
g:= func< n,a,b | f(n+1,a,b)-f(n,a,b) >;
A120151:= func< n | g(n,5,0) >;
[A120151(n): n in [1..60]]; // G. C. Greubel, Jun 15 2023
  • Maple
    a:= proc(n) option remember;
       5+floor(add(a(j)/3, j=1..n-1))
    end:
seq(a(n), n=1..44);  # Alois P. Heinz, Jun 16 2023
  • Mathematica
    nxt[{t_,n_}]:=Module[{c=Floor[(15+t)/3]},{t+c,c}]; NestList[nxt,{5,5},40][[All,2]] (* Harvey P. Dale, Jun 19 2022 *)
  • SageMath
    @CachedFunction
def A120151(n): return 5 + (sum(A120151(k) for k in range(1, n)))//3
[A120151(n) for n in range(1, 61)] # G. C. Greubel, Jun 15 2023

A120152 a(n) = 6 + floor((1 + Sum_{j=1..n-1} a(j))/3).

Original entry on oeis.org

6, 8, 11, 14, 19, 25, 34, 45, 60, 80, 107, 142, 190, 253, 337, 450, 600, 800, 1066, 1422, 1896, 2528, 3370, 4494, 5992, 7989, 10652, 14203, 18937, 25249, 33666, 44888, 59850, 79800, 106400, 141867, 189156, 252208, 336277, 448370
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Magma
    function f(n,a,b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/3);
    end for;
  return t;
end function;
g:= func< n,a,b | f(n+1,a,b)-f(n,a,b) >;
A120152:= func< n | g(n,6,1) >;
[A120152(n): n in [1..60]]; // G. C. Greubel, Jun 15 2023
  • Mathematica
    Module[{lista={6}},Do[AppendTo[lista,Floor[(19+Total[lista])/3]],{40}];lista] (* Harvey P. Dale, Jun 11 2013 *)
nxt[{s_,a_}]:=Module[{x=Floor[(19+s)/3]},{s+x,x}]; NestList[nxt,{6,6},40][[;;,2]] (* Harvey P. Dale, Mar 26 2023 *)
  • SageMath
    @CachedFunction
def A120152(n): return 6 + (1 + sum(A120152(k) for k in range(1,n)))//3
[A120152(n) for n in range(1, 61)] # G. C. Greubel, Jun 15 2023

A120153 a(n) = 7 + floor((2 + Sum_{j=1..n-1} a(j))/3).

Original entry on oeis.org

7, 10, 13, 17, 23, 31, 41, 55, 73, 97, 130, 173, 231, 308, 410, 547, 729, 972, 1296, 1728, 2304, 3072, 4096, 5462, 7282, 9710, 12946, 17262, 23016, 30688, 40917, 54556, 72741, 96988, 129318, 172424, 229898, 306531, 408708, 544944
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Magma
    function f(n,a,b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/3);
    end for;
  return t;
end function;
g:= func< n,a,b | f(n+1,a,b)-f(n,a,b) >;
A120153:= func< n | g(n,7,2) >;
[A120153(n): n in [1..60]]; // G. C. Greubel, Jun 15 2023
  • Mathematica
    nxt[{t_,a_}]:=Module[{c=Floor[(23+t)/3]},{t+c,c}]; Rest[Transpose[ NestList[ nxt,{0,7},40]][[2]]] (* Harvey P. Dale, Oct 08 2015 *)
  • SageMath
    @CachedFunction
def A120153(n): return 7 + (2 + sum(A120153(k) for k in range(1,n)))//3
[A120153(n) for n in range(1,61)] # G. C. Greubel, Jun 15 2023

A120154 a(n) = 9 + floor( Sum_{j=1..n-1} a(j)/3 ).

Original entry on oeis.org

9, 12, 16, 21, 28, 37, 50, 66, 88, 118, 157, 209, 279, 372, 496, 661, 882, 1176, 1568, 2090, 2787, 3716, 4955, 6606, 8808, 11744, 15659, 20879, 27838, 37118, 49490, 65987, 87983, 117310, 156414, 208552, 278069, 370759, 494345, 659127
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Magma
    function f(n,a,b)
  t:=0;
    for k in [1..n-1] do
       t+:= a+Floor((b+t)/3);
     end for;
  return t;
end function;
g:= func< n,a,b | f(n+1,a,b)-f(n,a,b) >;
A120154:= func< n | g(n,9,0) >;
[A120154(n): n in [1..60]]; // G. C. Greubel, Jun 20 2023
  • Mathematica
    A120154[n_]:= A120154[n]= 9 +Quotient[Sum[A120154[k], {k,n-1}], 3];
Table[A120154[n], {n,60}] (* G. C. Greubel, Jun 20 2023 *)
  • SageMath
    @CachedFunction
def A120154(n): return 9 + (sum(A120154(k) for k in range(1,n)))//3
[A120154(n) for n in range(1,61)] # G. C. Greubel, Jun 20 2023
Previous Showing 31-40 of 82 results. Next

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